My experience in these areas is mostly with color neg and print, in what you might call industrial-scale processing. In RA-4 process, regular fixer is not used on paper, rather bleach-fix is the preferred treatment. Anyway, similar modeling methods have been pretty reliable predictors. We would typically only screen results when a process was new, or for new materials, but a couple times a year we'd run "typical product" samples for image stability tests.

I doubt you'll have any problems with iodide in B&W papers, but I'm not certain. It's never an issue with color papers; replenished regeneration loops don't have any trouble with high reuse rates. Color film is a different story - multi-stage replenished fixer works fine, but any significant reuse (desilvered and regenerated) slows down the fix rate drastically (yep this is practical experience, it's presumably due to iodide build-up).

I'm not familiar with Ilford's replenishment method, so can't comment. But in general, I think one needs a certain amount of volume for replenishment to be cost effective, after that, it's got a lot of advantages.

Regarding Kodak's instructions to periodically discard (in 2-stage fixing), I've never understood why. In my experience, Kodak's info is pretty reliable, but they seem to prefer to err on the conservative (safe for the customer) side. So possibly they came across some odd customer situation and made the universal rec to discard so as to head off possible problems. But I'm just guessing.